Mechanism of Post-Radiation-Chemical Graft Polymerization of Styrene in Polyethylene

Article Mechanism of Post-Radiation-Chemical Graft Polymerization of Styrene in Polyethylene

Anatoly E. Chalykh 1,*, Vladimir A. Tverskoy 2, Ali D. Aliev 1, Vladimir K. Gerasimov 1, Uliana V. Nikulova 1 , Valentina Yu. Stepanenko 1 and Ramil R. Khasbiullin 1

1 Frumkin Institute of Physical Chemistry and Electrochemistry of Russian Academy of Sciences, Leninsky pr. 31-4, 119071 Moscow, Russia; [email protected] (A.D.A.); [email protected] (V.K.G.); [email protected] (U.V.N.); [email protected] (V.Y.S.); [email protected] (R.R.K.) 2 Lomonosov Institute of Fine Chemical Technologies, MIREA—Russian Technological University, Vernadsky Avenue 78, 119454 Moscow, Russia; [email protected] * Correspondence: [email protected]

Abstract: Structural and morphological features of graft polystyrene (PS) and polyethylene (PE) copolymers produced by post-radiation chemical polymerization have been investigated by methods of X-ray microanalysis, electron microscopy, DSC and wetting angles measurement. The studied samples differed in the degree of graft, iron(II) sulphate content, sizes of PE films and distribution of graft polymer over the polyolefin cross section. It is shown that in all cases sample surfaces are enriched with PS. As the content of graft PS increases, its concentration increases both in the volume and on the surface of the samples. The distinctive feature of the post-radiation graft polymerization is the stepped curves of graft polymer distribution along the matrix cross section. A probable reason for such evolution of the distribution profiles is related to both the distribution of Citation: Chalykh, A.E.; Tverskoy, V.A.; Aliev, A.D.; Gerasimov, V.K.; peroxide groups throughout the sample thickness and to the change in the monomer and iron(II) salt Nikulova, U.V.; Stepanenko, V.Y.; diffusion coefficients in the graft polyolefin layer. According to the results of electron microscope Khasbiullin, R.R. Mechanism of investigations and copolymer wettability during graft polymerization, a heterogeneous system is Post-Radiation-Chemical Graft formed both in the sample volume and in the surface layer. It is shown that the melting point, glass Polymerization of Styrene in transition temperature and degree of crystallinity of the copolymer decreases with the increasing Polyethylene. Polymers 2021, 13, 2512. proportion of graft PS. It is suggested that during graft polymerization a process of PE crystallite https://doi.org/10.3390/ decomposition (melting) and enrichment of the amorphous phase of graft polymer by fragments of polym13152512 PE macromolecules occurs spontaneously. The driving force of this process is the osmotic pressure exerted by the phase network of crystallites on the growing phase of the graft PS. Academic Editor: Shazed Aziz

Keywords: post effect radiation graft polymerization; alkoxyradicals; graft polymer distribution Received: 1 July 2021 proﬁle; morphology; graft polymer structure; degree of crystallinity; graft polymer melting Accepted: 26 July 2021 Published: 30 July 2021

Publisher’s Note: MDPI stays neutral 1. Introduction with regard to jurisdictional claims in published maps and institutional afﬁl- Graft polymerization is one of the effective methods for modifying the colloidal– iations. chemical, physical–chemical and performance properties of polymeric materials. Depending on the nature of the monomer, the conditions of graft polymerization and the degree of graft, it is possible to modify the surface layers of polymer material, its volume, and the uniform or gradient distribution of graft polymer over the thickness of a polymer matrix [1–4].

Copyright: © 2021 by the authors. Radiation graft polymerization allows the introduction of functional groups into poly- Licensee MDPI, Basel, Switzerland. mers of various kinds by the direct graft polymerization of monomers, such as acrylic This article is an open access article acid [1,5], vinylpyridines [6,7], acrylonitrile and others [8], or by the subsequent chemical distributed under the terms and modiﬁcation of graft polymers [5,9,10]. The latter include PS, the chemical modiﬁcation conditions of the Creative Commons of which allows the introduction of a wide range of functional groups into its struc- Attribution (CC BY) license (https:// ture. Radiation graft polymerization on low density polyethylene (LDPE) is the most creativecommons.org/licenses/by/ studied [1,5,8,11,12]. 4.0/).

Polymers 2021, 13, 2512. https://doi.org/10.3390/polym13152512 https://www.mdpi.com/journal/polymers Polymers 2021, 13, 2512 2 of 18

Among various methods of graft polymerization [3], such as “direct” graft, “post effect” graft under irradiation of polymer in a vacuum, inert atmosphere or in air, the “post effect” radiation graft polymerization under irradiation of polymer in air is characterized by its simplicity and high reproducibility. In this case, the polymerization is initiated by alkoxy radicals generated during the decomposition of hydro- and diperoxides. As a rule, salts of variable valence metals are added to the monomer solution as peroxide reducing agents to lower the polymerization temperature. Usually these are iron(II) salts [1,8]. In [9,13–16], sulfonated membranes obtained by such a method of graft polymerization of styrene on PE film for CO2/N2, alkane/olefin mixtures separation and proton conducting membranes for fuel cells are used. However, currently, the studies on influence of graft polymerization parameters on the distribution of graft PS over the cross section of the polymer matrix on PE films of different thicknesses irradiated in air are almost absent. Previously, such studies were carried out only for thin (up to 20 µm) PE films [6,17]. This information is of fundamental importance in the development of technology for the manufacture of asymmetric hybrid membranes for gas separation, namely, when choosing a mathematical model of hybrid membranes. This work presents the results of an investigation of the effects of the phase structure, morphology and distribution of graft PS in LDPE films up to 200 µm thick on “post effect” radiation graft polymerization in a wide range of graft degrees (composition of graft polymer). The results of the studies of the phase structure of graft PS in LDPE presented in this work allow us to specify more exactly the mechanism of styrene post-polymerization in a polyethylene matrix.

2. Experimental

Industrial LDPE films with Mw of 49 kDa, Mw/Mn = 11.4 and a refractive index at 130 ◦C of 1.4386 (NizhnekamskOrgSintez Inc., Nizhnekamsk, Russia) were used as objects of the study. The thickness of the films varied, ranging from 20 to 200 µm, and the size of the films was 2 × 5 cm. The samples were not treated before irradiation. The inhibitor was removed from styrene by 30% aqueous solution of KOH, and then washed with water to pH 7, dried over calcium chloride and distilled twice in a vacuum [1,5]. The PE samples were irradiated using a 60Co K-300.500 γ-radiation source at dose rates of 0.0043 Gy/s and from 10 to 100 kGy. The irradiation was performed in air at room temperature. The samples were washed with toluene to constant mass at the end of graft polymerization. Radiation–chemical graft polymerization of styrene in LDPE samples was carried out by the “post effect” method from a mixture of monomer with methanol. Polymerization was carried out in an open ampoule equipped with a thermoelectric cooler. The process temperature was 80 ◦C and was due to the boiling point of the solution containing iron(II) sulfate. As a rule, in this irradiation method, metal salts of variable valence are added as peroxide reducing agents to the monomer solution to reduce the temperature of polymerization [18]. These are usually iron(II) salts [19]. At the end of graft, the films were washed of monomer, homopolymer and iron salts by successive soaking in toluene and methanol and were then air dried to constant mass. The amount of graft PS (∆P) was determined by gravimetry as film weight gain (∆m) per unit mass of the original PE film (m0) (g of graft PS per mass of PE film):

(m − m ) ∆P = 1 0 × 100%. (1) m0 The characteristics of the studied objects are shown in Table1. Polymers 2021, 13, 2512 3 of 18

Table 1. Characteristics of PE ﬁlms with graft PS.

Composition of Composition of Amount of Graft PS Graft Polymer, Amount of Graft PS Graft Polymer, Sample Sample (g PS/100 g PE) PS Mass Fraction (g PS/100 g PE) PS Mass Fraction (ωPS) (ωPS) PE/PS16 16 0.14 PE/PS248 248 0.71 PE/PS26 26 0.20 PE/PS271 271 0.73 PE/PS47 47 0.32 PE/PS348 348 0.78 PE/PS96 96 0.49 PE/PS405 405 0.80

EPR spectra were taken on a standard radio spectrometer RE-1306 (Chernogolovka, Russia). The distribution of oxygen-containing compounds throughout the PE film thickness, including peroxide formation, was determined using a comparative analysis of the optical density of 1720 cm−1 band (C=O valence vibrations in oxidized PE [8]) versus the optical density of 1475 cm−1 band (C–H asymmetric deformation vibrations in PE [5]) taken as an internal standard in IR transmission and attenuated total reflection (ATR) spectra. IR spectra were recorded on Perkin–Elmer-580 spectrophotometers (Stockholm, Sweden). ATR spectra were obtained using a KRS-5 crystal with an incidence angle of 45◦ and a scanning depth of ~5 µm. Selective contrasting (sulfonation) of graft polystyrene chains was carried out at a temperature of 98 ◦C with concentrated (96 wt.%) sulfuric acid. At the end of the process, the films were washed with sulphuric acid solutions of decreasing concentrations and distilled water. Sulfonation with a chlorosulfonic acid complex with 1,4-dioxane was carried out in 1,2-dichloroethane at room temperature. The films were then boiled in distilled water to convert the sulphochloride groups to sulphonic acid groups, washed in distilled water and air dried. In all cases, exhaustive sulfonation of phenyl radicals was achieved, the degree of which was monitored by weight gain, similar to the degree of graft. The characteristics of the thus obtained samples are presented in Table2.

Table 2. Characteristics of the sulfated PE ﬁlms with graft PS.

Amount Graft PS PS Content, Mass [–SO H]/[St] Sample 3 (g PS/100 g PE) Fraction g-eq/mol-unit PE/PS16 16 0.14 0.53 PE/PS47 47 0.32 0.30 PE/PS96 96 0.49 0.16 PE/PS16 16 0.14 1.79 PE/PS47 47 0.32 1.3 PE/PS96 96 0.49 1.5

Differential scanning calorimetry (DSC). This method was used to record the thermal effects accompanying the melting (crystallization) and glass transition of the graft copolymer under conditions of programmed temperature change. The heating rate varied from 4 to 50 deg/min. Measurements were performed on a DSC 204 F1 Phoenix (Netzsch, Selb, Germany) in the temperature range from −40 to 150 ◦C. All experiments were performed on sample weights of at least 5 mg. For automatic processing of measurement results, we used “Proteus Analysis” software, in which the Tg value was determined as an inﬂection point of the ∆Cp (T) curve, and the Tm value as a maximum (peak) point. The area of the peak, bounded by the DSC curve and the zero baseline, was taken to be equal to the change in melting enthalpy (∆Hm). To determine the glass transition temperature, we also used the tangent method [20], which was applied to the left, right and middle parts of the heat capacity step ∆Cp (T). Polymers 2021, 13, 2512 4 of 18

The crystallinity degree of the studied samples was determined from the equation:

∆H α = (2) ∆H100%

where ∆H is the melting enthalpy of the studied sample; ∆H100% is the melting enthalpy for a fully crystalline polymer and ∆H100% = 293 J/g [21]. The structural–morphological characteristics of the graft copolymers were studied by transmission electron microscopy, scanning electron microscopy, and X-ray microanalysis. In the first case, the outer surface of the graft films was used as the study object, which was subjected to etching in high frequency oxygen plasma in order to reveal the supramolecular structure. Oxygen pressure in the etching zone was 0.03 mm Hg, electron energy was 2–3 eV, etching time was 15–20 min, generator power was 100 W, and the frequency was 10 MHz. The morphology of the etched surfaces was examined via a method of one-step carbon-platinum replicas using a transmission electron microscope (TEM-301 (Amsterdam, The Netherlands)) at an accelerating voltage of 80 keV. The phases were identified by X-ray microanalysis using the characteristic Kα radiation of the sulfur line. In the case of scanning microscopy and X-ray microanalysis, the studies were carried out on cross sections of the sulfated PE film with the graft PS (Figure1) obtained on the LKB cryo ultramicrotome. Surface analysis was performed on a JSM-U3 scanning electron microscope (JEOL, Tokyo, Japan) at an accelerating voltage of 5–7 keV equipped with an energy dispersive spectrometer EUMEX (Hamburg, Germany). The size of the electron beam is 10 nm, the current is 10−10 Å and the resolution of the method is 1.3 µm, calculated using the Reed nomogram for contrasted PS samples. These parameters made it possible to obtain information on the cross-sectional distribution of samples of various thicknesses. Figure1 shows a typical cross section micrograph of a PE film with the graft PS obtained in secondary electrons. It can be seen that the graft layer differs slightly in contrast to the central part. The distribution of the characteristic X-ray emission of the Kα sulfur line shows the change in the PS concentration upon transition from the surface layers of the film to its center. P To measure the surface energy of the graft copolymers (γlv), its polar (γ lv) and disper- D sion components (γ lv), the wetting angle measurement method was used, employing a set of liquids with known characteristics (Table3). A drop of liquid with a volume of 1.10 −3 to 1.10−2 cm3 was deposited onto the surface of the polymer sample using a microsyringe. Contact angles were determined on the Easy Drop device (KRUSS, Hamburg, Germany)). All measurements were performed at room temperature. The data obtained by the wetting angle method were processed via the standard instrument software using the well-known Owens and Wendt equation [22,23].

Table 3. Characteristics of the probe liquids [23].

3 ◦ P 2 D 2 2 № Liquid d, g/cm Tboil, C γ lv, mJ/m γ lv, mJ/m γlv, mJ/m 1 Water 1.0 100.0 50.2 22.0 72.2 3 Ethyleneglycol 1.1090 197.2 19.0 29.3 48.3 4 o-Tricresyl phosphate 1.165 263.0 4.5 36.2 40.7 5 Pyridine 0.9819 115.4 0.8 37.2 38.0 6 Decane 0.730 174.1 0.0 23.9 23.9 PolymersPolymers 20212021,, 1313,, x 2512 FOR PEER REVIEW 55 of of 20 18

FigureFigure 1. 1. MicrophotographMicrophotograph of of a a cross cross section section of of a a sulfated sulfated PE film ﬁlm with graft PS with ωPS == 0.42 0.42 in in secondarysecondary electrons electrons (a (a) )and and the the profile proﬁle of of the the characteristic characteristic radiation radiation distribution distribution of of the the K KααSS line line (contrasted(contrasted graft graft PS) PS) along along the the cross cross section section of of the the sample sample ( (bb).). A A is is the the area area where where the the target target replica replica was obtained. was obtained.

3. ResultsTo measure and Discussion the surface energy of the graft copolymers (γlv), its polar (γPlv) and dis- D persionIt iscomponents known [1– (4γ] thatlv), the the wetting irradiation angle of measurement polyoleﬁns inmethod air is accompaniedwas used, employing by their aradiation–chemical set of liquids with oxidation.known characteristics Radiation oxidation (Table 3). is A a chaindrop processof liquid and with is describeda volume of by 1.10the− following3 to 1.10−2 cm scheme3 was (Figuredeposited2). onto the surface of the polymer sample using a microsyringe.The Contact process angles of graftwere polymerizationdetermined on the can Easy be initiated Drop device by both (KRUSS, trapped Hamburg, hydrocarbon Ger- many)).radicals All and measurements peroxide radicals were and performed hydroperoxides. at room Intemperature. our case, the The polymerization data obtained was by theinitiated wetting by angle alkoxy method radicals were formed processed during via the the decomposition standard instrument of hydro- software and diperoxides using the well-known(Figure2b). TheOwens concentration and Wendt of equation alkoxy radicals[22,23]. initiating graft polymerization depends not only on the concentration of peroxides, but also on the concentration of iron(II) salt, which servesTable 3. not Characteristics only as an inhibitor of the probe of styreneliquids [23]. homopolymerization in the graft solution, but also as a reducing agent of hydro- and diperoxides that decompose in the interaction № Liquid d, g/cm3 Tboil, °C γPlv, mJ/m2 γDlv, mJ/m2 γlv, mJ/m2 with the iron(II) salt ions into alkoxy radicals and hydroxide or alkoxy anions. 1 Water 1.0 100.0 50.2 22.0 72.2 The content of each of these types of active polymerization centers in the polymer 3 Ethyleneglycol 1.1090 197.2 19.0 29.3 48.3 depends on the irradiation dose and dose rate, temperature and oxygen concentration 4 o-Tricresyl phosphate 1.165 263.0 4.5 36.2 40.7 during the irradiation and storage of the polymer, its degree of crystallinity, thickness, 5 Pyridine and other 0.9819 factors. Studies115.4 [6] of the EPR spectra 0.8 of 20 µm-thick 37.2 PE ﬁlms irradiated 38.0 by 6 Decane an electron 0.730 beam to a dose174.1 of 50 kGy showed 0.0 that peroxide 23.9 radicals are mainly23.9 present

Polymers 2021, 13, 2512 6 of 18

Polymers 2021, 13, x FOR PEER REVIEW 6 of 20

in such thin samples,3. Results and the and appearance Discussion and shape of these spectra [7] are virtually the same for all irradiationIt doses. is known One [1–4] hour that the after irradiation irradiation, of polyolefins the concentration in air is accompanied of trapped by their 19 peroxyradicals in theradiation–chemical ﬁlm is 0.4 × 10 oxidation.spin/g Radiation and changes oxidation littleis a chain thereafter. process and Thus, is described it was by found that after 1 monththe following of storage scheme it (Figure was 0.1 2).× 1019 spin/g.

Figure 2. Scheme of radiation–chemical oxidation of PE (a), formation of alkoxide radicals (b), and growth of the graft Figure 2. a b polymer chainScheme (c). of radiation–chemical oxidation of PE ( ), formation of alkoxide radicals ( ), and growth of the graft polymer chain (c). The process of graft polymerization can be initiated by both trapped hydrocarbon The polymer peroxidesradicals and formedperoxide radicals as a result and hydroper of radiationoxides. In oxidation our case, the are polymerization quite stable, was their concentration remainsinitiated by unchanged alkoxy radicals during formed film during storage, the decomposition which was of hydro- confirmed and diperoxides by the (Figure 2b). The concentration of alkoxy radicals initiating graft polymerization depends reproducibility of thenot results only on on the styrene concentration graft of onto peroxides, these filmsbut also over on the 4 months.concentration The of degree iron(II) ofsalt, graft PS varied in thewhich range serves of 135not only÷ 140%. as an inhibitor of styrene homopolymerization in the graft solution, We studied thebut distribution also as a reducing of oxygen-containing agent of hydro- and diperoxides compounds, that decompose including in peroxides,the interaction over the thickness ofwith PE the films iron(II) modified salt ions into by irradiationalkoxy radicals using and hydroxide the ratio or ofalkoxy the valuesanions. of the The content−1 of each of these types of active polymerization centers in the polymer optical density of thedepends 1720 on cm the irradiationband (C=O dose valenceand dose vibrationsrate, temperature in oxidized and oxygen PE concentration [8]) and −1 the 1475 cm bandduring (C–H the asymmetric irradiation and strain storage vibrations of the polymer, in PE its [degree5]), taken of crystallinity, as an internal thickness, standard in the IR transmissionand other factors. and Studies ATR [6] spectra. of the EPR It spectra turned of out20 μm-thick that this PE films ratio irradiated calculated by an from the ATR spectraelectron is 1.7 beam times to higher a dose of than 50 kGy that showed calculated that peroxide from the radicals transmission are mainly spectra.present in such thin samples, and the appearance and shape of these spectra [7] are virtually the Because the ATR methodsame for examines all irradiation the surface,doses. One and hour the after transmission irradiation, the method concentration examines of trapped the entire volume of theperoxyradicals sample, then in we the can film talk is 0.4 about × 1019 aspin/g significant and changes predominance little thereafter. of peroxideThus, it was groups in the surfacefound layers. that after 1 month of storage it was 0.1 × 1019 spin/g. A similar result followsThe polymer from peroxides a comparison formed as of a result the PEof radiation water wettingoxidation are angles quite stable, of 102 their◦ before irradiation andconcentration 87◦ after remains irradiation unchanged and theduring polar film componentstorage, which ofwas 0.57 confirmed (before) by andthe reproducibility of the results on styrene graft onto these films over 4 months. The degree of 2 3.4 (after) mJ/m . Thegraft lowerPS varied value in the ofrange the of contact135 ÷ 140%. angle and the increased value of the polar component unambiguouslyWe studied the testify distribution to the of polarity oxygen-cont ofaining the modified compounds, PE in surface.cluding peroxides, Thus, it can be stated that,over as athe result thickness of irradiation, of PE films modified the surface by irradiation of PE using samples the ratio is enrichedof the values with of the −1 oxygen-containing compounds,optical density of including the 1720 cm peroxides band (C=O [24 valence], to avibrations greater in extent oxidized as PE compared [8]) and the 1475 cm−1 band (C–H asymmetric strain vibrations in PE [5]), taken as an internal standard to their volume. Wein the found IR transmission that the radiationand ATR spectra. yield It ofturned oxygen-containing out that this ratio calculated compounds from the slightly decreases withATR increasingspectra is 1.7 sampletimes higher thickness than that over calculated 100 µ fromm, which the transmission should bespectra. taken Be- into account when analyzingcause the ATR the method products examines of graft the surface, polymerization and the transmission [25,26]. method examines the Figure3 showsentire typical volume kinetic of the curves sample, of then styrene we can grafttalk about onto a significant PE under predominance different condi- of peroxide groups in the surface layers. tions of the process. It wasA similar found result that follows the from irradiation a comparison dose of D the in PE the water studied wetting range angles ofof 102° D values from 10 to 250before kGy irradiation has little and effect 87° onafter the irradiation course and of the the graftpolar component polymerization of 0.57 (before) process. and The introduction of3.4 different (after) mJ/m amounts2. The lower of value iron(II) of the sulfate contact angle into and the the reaction increased system value of inthe thepolar concentration rangecomponent from 3 to unambiguously 10 g/L only changestestify to the the polarity graft of rate. the modified At higher PE concentrationssurface. Thus, it can of iron(II) sulfate, the graft rate decreases by 20–25%. The extreme dependence of the initial polymerization rate on the concentration of iron(II) salt at a constant irradiation

dose is related to the fact that iron(II) ions are not only co-initiators, reducing peroxides to alkoxy radicals, but also inhibitors of graft polymerization, interacting with primary and growing radicals: −RO• + Fe2+ → −RO− + Fe3+ −R• + Fe2+ → −R− + Fe3+ Polymers 2021, 13, x FOR PEER REVIEW 7 of 20

be stated that, as a result of irradiation, the surface of PE samples is enriched with oxygen- containing compounds, including peroxides [24], to a greater extent as compared to their volume. We found that the radiation yield of oxygen-containing compounds slightly decreases with increasing sample thickness over 100 μm, which should be taken into account when analyzing the products of graft polymerization [25,26]. Figure 3 shows typical kinetic curves of styrene graft onto PE under different conditions of the process. It was found that the irradiation dose D in the studied range of D values from 10 to 250 kGy has little effect on the course of the graft polymerization process. The introduction of different amounts of iron(II) sulfate into the reaction system in the concentration range from 3 to 10 g/L only changes the graft rate. At higher concentrations of iron(II) sulfate, the graft rate decreases by 20–25%. The extreme dependence of the initial polymerization rate on the concentration of iron(II) salt at a constant irradiation dose is related to the fact that iron(II) ions are not only co-initiators, reducing peroxides to alkoxy radicals, but also inhibitors of graft polymerization, interacting with primary and growing radicals: –RO• + Fe2+ → –RO− + Fe3+

Polymers 2021, 13, 2512 7 of 18 –R• + Fe2+ → –R− + Fe3+

Figure 3. Kinetic curves of styrene graft onto PE under different conditions of the process. Results of

gravimetric integral measurements. [FeSO4·7H2O] content of 2 (1), 3 (2), 10 (3) g/L. Film thickness Figure 3. Kinetic curves of styrene graft onto PE under different conditions of the process. Results 140 µm, radiation dose 0.14 Gy. of gravimetric integral measurements. [FeSO4·7H2O] content of 2 (1), 3 (2), 10 (3) g/L. Film thickness 140 μm,Using radiation information dose 0.14 Gy. on the concentration of peroxyradicals in the PE film ~0.4 × 1019 spin/g, we estimated the degree of graft PS under the assumption of predominant mono- 19 molecularUsing information filling of the on graft the centers concentration with a monolayer of peroxyradicals of styrene in molecules. the PE film The ~0.4 numerical × 10 spin/g,value we is plottedestimated with the a degree dotted of line graft (in PS Figure under3, athe line assumption parallel to of the predominantx-axis) on mono- the real molecularkinetic curve filling of of the the graft. graft It centers can be with seen a that, monolayer already of in styrene the initial molecules. part of the The process, numeri- we calcan value expect is plotted the filling with of a all dotted centers line of (in graft Figure polymerization. 3, a line parallel to the x-axis) on the real kineticFrom curve the of macroscopicthe graft. It can point be ofseen view, that, in thealready region in ofthe low initial graft part degrees of the (up process, to 40 wt.%), we canthe expect amount the offilling graft of PS all increases centers of linearly graft polymerization. with time. At the same time, no anomalies are observedFrom the that macroscopic would suggest point specific of view, features in th ofe theregion structural of low organization graft degrees of the(up graft to 40 PS wt.%),layers the in amount PE films of of graft different PS increases thicknesses, linearly despite with the time. fact At that the the same fraction time, of no graft anomalies polymer significantly exceeds the solubility limit of PS in PE (Figure4)[27]. Figure5 shows PS distribution profiles for samples with different graft degrees obtained under close graft polymerization conditions. It can be seen that, in all cases, the sample surfaces are enriched with PS. At the same time, the PS distribution profiles within the films differ significantly from each other. Thus, at irradiation doses of 10 and 60 kGy, a uniform distribution of PS over the entire sample thickness is realized, that is, a combined three-layer system is formed (Figure5). Further, as the content of the graft PS increases, its concentration increases both in the volume and on the surface of the samples. A linear correlation between the fraction of graft polymer and the relative concentration of the contrasted polymer is maintained (Figure6). In our opinion, this result suggests that the mechanisms of graft polymerization on the surface and in the volume of PE samples are identical. In this case, samples of different thicknesses fit into a general linear relationship. Polymers 2021, 13, x FOR PEER REVIEW 8 of 20

Polymers 2021, 13, 2512 are observed that would suggest specific features of the structural organization of the graft 8 of 18 PS layers in PE films of different thicknesses, despite the fact that the fraction of graft polymer significantly exceeds the solubility limit of PS in PE (Figure 4) [27].

Polymers 2021, 13, x FOR PEER REVIEWFigureFigure 4. 4. FragmentFragment of ofthe the diagram diagram of solubility of solubility of PSof in PSPE in[27]. PE The [27 dotted]. The dottedline corresponds line corresponds to the9 of 20 to the

movementmovement of of the the system system figurative ﬁgurative point point upon upon styrene styrene polymerization. polymerization.

Figure 5 shows PS distribution profiles for samples with different graft degrees obtained under close graft polymerization conditions. It can be seen that, in all cases, the sample surfaces are enriched with PS. At the same time, the PS distribution profiles within the films differ significantly from each other. Thus, at irradiation doses of 10 and 60 kGy, a uniform distribution of PS over the entire sample thickness is realized, that is, a combined three-layer system is formed (Figure 5). Further, as the content of the graft PS increases, its concentration increases both in the volume and on the surface of the samples. A linear correlation between the fraction of graft polymer and the relative concentration of the contrasted polymer is maintained (Figure 6). In our opinion, this result suggests that the mechanisms of graft polymerization on the surface and in the volume of PE samples are identical. In this case, samples of different thicknesses fit into a general linear relationship.

FigureFigure 5. Distribution 5. Distribution proﬁles profiles of graft of graft PS inPS PE. in PE. PE ﬁlmPE film thickness thickness is 100is 100µm. μm. Graft Graft degree degree∆ ΔPP = = 55 (a(a)) andand 130130 wt.%wt.% ( b).). Graft from styrene/methanolGraft from styrene/methanol mixture mixt (80/20ure %vol).(80/20 %vol). Radiation Radiation dose dose−60 − kGy.60 kGy. [FeSO [FeSO4·7H4·7H2O]2O] concentrationconcentration = =10 10 g/L. g/L.

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Figure 6. Correlation dependence of the profile intensity in the center of the film relative to maximum Figure 6. Correlation dependence of the profile intensity in the center of the film relative to maxi- intensity on the concentration of graft PS. The thickness of the films is 200 µm (black dots), 20–50 µm mum intensity on the concentration of graft PS. The thickness of the films is 200 μm (black dots), µ 20–50(gray μ dots),m (gray 120–150 dots), 120–150m (white μm dots). (white dots). A distinctive feature of post effect graft polymerization is, as it seems to us, the stepped A distinctive feature of post effect graft polymerization is, as it seems to us, the form of PS distribution curves, which is preserved up to ∆P = 150 wt.%, on the one hand, stepped form of PS distribution curves, which is preserved up to ΔP = 150 wt.%, on the and the distribution pattern of the graft polymer in the film volume, on the other hand. At one hand, and the distribution pattern of the graft polymer in the film volume, on the irradiation doses of 100 kGy, the distribution pattern of the graft polymer in the sample other hand. At irradiation doses of 100 kGy, the distribution pattern of the graft polymer volume changes from linear (Figure7a) to parabolic (Figure7b). It can be assumed that, in the sample volume changes from linear (Figure 7a) to parabolic (Figure 7b). It can be under these polymerization conditions, there is a diffusive decline in the concentration of assumed that, under these polymerization conditions, there is a diffusive decline in the PS in the PE matrix with increased distance from the surface. concentrationA probable of PS reason in the for PE this matrix evolution with increased of the distribution distance from profiles the of surface. the graft PS may be related both to the distribution of peroxide groups over the sample thickness and to the changes in the translational diffusion coefficients of monomer and iron(II) salt in the graft PS layer and PE matrix. Indeed, as shown above, the surface layers of PE films always possess a higher concentration of peroxide groups, and hence a higher concentration of graft polymer, regardless of the irradiation dose, styrene concentration and iron(II) sulfate concentration. It should be added that methanol is a precipitator of PS. It follows that the growing PS chains have a different conformation on the surface and in the volume of the film. On the film’s surface, they have the conformation of a coiled ball or globule with occluded growing macroradicals. While in the film volume, where the concentration of methanol is much lower, the growing macroradicals probably have the conformation of a swollen ball. In the first case, quadratic polymerization termination is difficult due to the low mobility of the growing PS chains; in contrast, inside the film, where the growing chains have high mobility, quadratic polymerization termination is possible. However, the linear nature of the macroscopic kinetics of graft polymerization allows us to speak about the occlusion of growing macroradicals throughout the volume of the graft polymer, which is associated with its glassy state.

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FigureFigure 7. 7.The The effect effect of of radiation radiation dose dose on on sulfur sulfur distribution distribution proﬁle profile in in PE PE with with graft graft PS. PS. PE PE ﬁlm film thickness thickness is is 140 140µ μm.m. Graft Graft fromfrom styrene/methanol styrene/methanol mixture mixture (70/30 (70/30 vol.%).vol.%). [FeSO4·7H·7H22O]O] concentration concentration is is 3 3 g/L. g/L. Δ∆P P= =30%. 30%. Irradiation Irradiation dose, dose, kGy: kGy: 10 10 (a) (aand) and 100 100 (b ().b ).

WeA probable attribute thereason presence for this of theevolution graft polymer of the distribution concentration profiles jump between of the graft the surfacePS may andbe related the volume both to the the distribution high value ofof thepero styrenexide groups diffusion over coefficientthe sample in thickness the PE matrix and to ∼ −7 2 (estimatesthe changes showed in the that translational D = 10 cmdiffusion/s), and coefficients the near-surface of monomer layer, whichand iron(II) is ~10 µsaltm thick,in the doesgraft not PS resistlayer theand monomerPE matrix. migration. Indeed, as Thus,shown it above, can be the assumed surface that, layers at thisof PE stage, films the al- graftways polymerization possess a higher proceeds concentration in the of kinetic peroxi regionde groups, with and a constant hence a higher rate of concentration the process. Sinceof graft the polymer, process regardless is realized of under the irradiation conditions dose, of significant styrene concentration monomer excess,and iron(II) we can sul- assumefate concentration. that the concentration It should be of added peroxide that radicals methanol isconstant, is a precipitator which confirmsof PS. It follows the above- that mentionedthe growing assumption PS chains abouthave a their different occlusion conformation by the PS on phase. the surface In addition, and in at the this volume stage of of post-polymerization,the film. On the film’s the surface, transverse they dimensionshave the conformation of the samples of a do coiled not change.ball or globule with occludedIn the growing region of macroradicals. high graft degrees While∆P ≥in200%, the film when volume, the degree where of surfacethe concentration and volume of fillingmethanol reaches is much high lower, values the and growing the size macrorad of the near-surfaceicals probably layer have reaches the conformation 20 µm, the graft of a processswollen passes ball. In into the the first diffusion case, quadratic region of polymerization the process. Note termination that under theseis difficult conditions, due to the the low mobility of the growing PS chains; in contrast, inside the film, where the growing

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translational diffusion coefﬁcient decreases to 10−10 cm2/s. Probably, a certain contribution to this process is made by the formation of the chemical bonding network in the PE matrix. The results of structural–morphological studies are of signiﬁcant interest for the phase analysis of the system. Thus, according to the results of electron microscope studies, a heterogeneous two-phase system is formed both in the sample volume and in the surface layer during the graft polymerization (Figure8). It can be seen that the formation of the matrix (PE)-inclusion (PS) type with particle size of 1–3 µm, is observed both in the surface layer (Figure8a–c) and in the volume (Figure8d,e) in the area of low graft degrees (∆P ≤ 5%). As the graft degree increases, the PS particles coalesce to form macroscopically sized aggregates. Finally, at ∆P = 0.4, according to the PS-PE system phase state diagram, Polymers 2021, 13, x FOR PEER REVIEWthe area of phase reversal is observed. It is most vividly manifested in the surface layer13 of of 20

the graft samples.

(a) (d)

(b) (e)

FigureFigure 8. 8.Morphology Morphology of of the the surface surface ((aa––cc))and and thethe volumevolume ((dd––ff)) ofof thethe samplessamples ofof graftgraft copolymer.copolymer. ContentContent of of graft graft PS PS 16 16 ( a(,ad,d),), 47 47 ( b(b,e,)eи) и348% 348% (c (,cf).,f).

WettingWetting of of the the graft graft copolymer copolymer surface surface.. It It is is known known that that the the wetting wetting test test is is one one of of the the mostmost sensitive sensitive methods methods for for controlling controlling the the quality quality of hydrophobicof hydrophobic surfaces surfaces and and the the packing pack- densitying density of graft of macromoleculesgraft macromolecules [28]. To [28]. describe To describe the wettability the wettability of heterogeneous of heterogeneous surfaces containingsurfaces containing areas of two areas types, of two the types, equation the ofequation A. Cassie of andA. Cassie S. Baxter and [ 29S. ]:Baxter [29]: cos Θ = f cos Θ f cos Θ (3) cos Θ = f1 cos Θ1 + f2 cos Θ2 (3)

f1 +fff2 = 1,=1, (4)(4)

wherewhere f 1f1and and f 2f2are arefractions, fractions,occupied occupiedby by the the areas areas with with wetting wetting angles anglesΘ Θ11and andΘ Θ22.. Indexes “1” and “2” denote PE and PS phases. Using Equations (3) and (4), as well as the surface wetting data of the graft samples (Figure 9, curve 1), the fraction of the surface occupied by PS molecules depending on the graft degree was estimated. It can be seen that the water wetting angle (sessile) for the hydrophilic–hydrophobic copolymer surface depends on the degree of PS graft and is at the level of 87–100°. The wetting angles plateau at ΔP = 0.6 and Θ ≥ 93°. The fraction of the surface occupied by PS macromolecules increases continuously with increasing degree of graft and reaches 80% for PE-PS samples with ΔP ≥ 0.8.

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Indexes “1” and “2” denote PE and PS phases. Using Equations (3) and (4), as well as the surface wetting data of the graft samples (Figure9, curve 1), the fraction of the surface occupied by PS molecules depending on the graft degree was estimated. It can be seen that the water wetting angle (sessile) for the hydrophilic–hydrophobic copolymer surface depends on the degree of PS graft and is at the level of 87–100◦. The wetting angles plateau ◦ Polymers 2021, 13, x FOR PEER REVIEWat ∆P = 0.6 and Θ ≥ 93 . The fraction of the surface occupied by PS macromolecules14 of 20

increases continuously with increasing degree of graft and reaches 80% for PE-PS samples with ∆P ≥ 0.8.

Figure 9. Calculated dependences of the fraction of the graft copolymer surface occupied by PS Figure 9. Calculated dependences of the fraction of the graft copolymer surface occupied by PS macromolecules (1) and water wetting angles (2) on the fraction of graft PS. macromolecules (1) and water wetting angles (2) on the fraction of graft PS. The results obtained are in good agreement with the data of structural–morphological The results obtained are in good agreement with the data of structural–morphologi- studies. Indeed, if the curve of the surface area occupied by PS macromolecules is to be cal studies. Indeed, if the curve of the surface area occupied by PS macromolecules is to plotted onto the phase diagram of the PE-PS system, then using this dependence one can be plotted onto the phase diagram of the PE-PS system, then using this dependence one obtain information about the trajectory of the ﬁgurative point of the system during graft polymerization.can obtain information Obviously, about at ∆theP ≥trajectory0.4, there of is the a phase figurative reversal point in theof the graft system surface during layer andgraft a polymerization. PS matrix inclusion Obviously, (PE) type at structureΔP ≥ 0.4,emerges, there is a which phase is reversal described in the above graft (Figure surface4). layerIt and is interesting a PS matrix to noteinclusion that the(PE) data type on structure the energy emerges, characteristics which is of described the graft layersabove (Figure 4). D (Table4)—the dispersion component of the surface energy γs —are in favor of denser packingIt is of interesting PS macromolecules to note that in the regiondata on of the high energy graft degreescharacteristics∆P ≥ 0.4, of whichthe graft indicates layers D a(Table more 4)—the perfect conformationaldispersion component order of of the the macromolecules. surface energy γs —are in favor of denser packing of PS macromolecules in the region of high graft degrees ΔP ≥ 0.4, which indicates Tablea more 4. perfectEnergy characteristicsconformational of theorder surface of the of PE-PSmacromolecules. samples with different degrees of graft.

2 D 2 P 2 Table 4. SampleEnergy characteristics ofγ sthe, mJ/m surface of PE-PS samplesγs , mJ/m with different degreesγs , mJ/mof graft. PE-PS16 30.72 30.15 0.57 Sample γs, mJ/m2 γsD, mJ/m2 γsP, mJ/m2 PE-PS26 30.31 29.60 0.71 PE-PS16PE-PS96 30.7237.96 30.1537.09 0.570.88 PE-PS271PE-PS26 30.3141.94 29.6041.23 0.71 PE-PS348PE-PS96 37.9640.69 37.0939.76 0.880.93 PE-PS271 41.94 41.23 0.71 PE-PS348 40.69 39.76 0.93

Additional information about the supramolecular organization of the graft copolymers was obtained by DSC. Figure 10 shows typical thermograms of PE and PS homopolymers. It can be seen that, for PE, as a partially crystalline polymer, there is a melting peak Tm and a small bend in the temperature dependence of the heat capacity in the glass transition region Tg. The heat capacity jump corresponds to ∆Cp = 0.041 J/g·K and a glass transition temperature of −24.5 °C. The beginning and end of melting correspond to 91 and 150 °C, respectively. The melting point of PE is 135.1 °C. Melting enthalpy (∆Hm, peak area) is 189.8 J/g, the crystallinity degree is 54.8%.

Polymers 2021, 13, x FOR PEER REVIEW 15 of 20

Polymers 2021, 13, 2512 13 of 18 The heat capacity jump associated with the glass transition of the polymer can be clearly identified in the temperature range of 103 ÷ 119 °C on the thermogram of the first heating of PS. The glass transition temperature of PS corresponds to 107.7 °C. The specific heat Additionalcapacity jump information is 0.329 aboutJ/g·K. theThe supramolecular thermogram of organization the second ofheating the graft (after copolymers thermal wasannealing) obtained shows by DSC. that Figureglass transition 10 shows is typical observed thermograms in the temperature of PE and range PS homopolymers. of 92 ÷ 112 °C, Itthe can value be seen of the that, glass for PE, transition as a partially temperature crystalline corresponds polymer, thereto 104.3 is a meltingK. The heat peak capacity Tm and ajump small at bendthis interval in the temperature is 0.363 J/g·K. dependence The comparison of the of heat the capacitythermograms in the presented glass transition in Fig- regionure 11 Tshowsg. The that heat the capacity region jump of PS corresponds glass transition to ∆ coincidesCp = 0.041 with J/g· Kthe and region a glass of the transition begin- temperature of −24.5 ◦C. The beginning and end of melting correspond to 91 and 150 ◦C, ning of PE crystallite melting. Obviously, this◦ effect makes it difficult to obtain infor- respectively.mation about Thethe phase melting structure point of of PE graft is 135.1 copolymers.C. Melting enthalpy (∆Hm, peak area) is 189.8 J/g, the crystallinity degree is 54.8%.

Figure 10. Typical thermograms for PE (1) and PS (2—first, 3—second heating) at a heating rate of 20 deg/min. Figure 10. Typical thermograms for PE (1) and PS (2—first, 3—second heating) at a heating rate of 20 deg/min. The heat capacity jump associated with the glass transition of the polymer can be The thermograms of the PE–PS16 sample show that, at a heating rate of 5 deg/min, clearly identified in the temperature range of 103 ÷ 119 ◦C on the thermogram of the first the glass transition is observed in the temperature range of 27 ÷ 40 °C, and the glass tran- heating of PS. The glass transition temperature of PS corresponds to 107.7 ◦C. The specific sition temperature is 35.2 °C. The heat capacity jump is equal to 0.426 J/g·K. The melting heat capacity jump is 0.329 J/g·K. The thermogram of the second heating (after thermal point of the crystalline part of the copolymer corresponds to 105.4 °C, and the melting annealing) shows that glass transition is observed in the temperature range of 92 ÷ 112 ◦C, enthalpy is 71 J/g. At a rate of 10 deg/min the glass transition interval shifts slightly to a the value of the glass transition temperature corresponds to 104.3 K. The heat capacity jump temperature of 22–48 °C, and the glass transition temperature is 47 °C. The heat capacity at this interval is 0.363 J/g·K. The comparison of the thermograms presented in Figure 11 showsjump at that this the interval region is of 0.472 PS glass J/g·K. transition coincides with the region of the beginning of PE crystalliteWith the melting. increase Obviously,of graft degree this effect(Figure makes 11) up it difficult to ωPS = to 0.49, obtain and information then up to about0.8 PS thefraction, phase glass structure transition of graft is observed copolymers. in the temperature range of 29 ÷ 50 °C, the glass tran- sitionThe temperature thermograms is 42.7 of the °C, PE–PS16 and the heat sample capacity show that,jump at is a − heating0.262 J/g·K. rate ofThe 5 deg/min,melting tem- the glassperature transition of the iscrystalline observed phase in the temperatureof the copolymer range corresponds of 27 ÷ 40 ◦ C,to and108 the°C, glassthe melting transition en- temperaturethalpy is 37.33 is 35.2J/g. ◦TheC. The values heat of capacity melting jump enthalpy is equal for toall 0.426 samples J/g·K. are The presented melting in point Table of the5. crystalline part of the copolymer corresponds to 105.4 ◦C, and the melting enthalpy is 71 J/g. At a rate of 10 deg/min the glass transition interval shifts slightly to a temperature of 22–48 ◦C, and the glass transition temperature is 47 ◦C. The heat capacity jump at this interval is 0.472 J/g·K.

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Figure 11. Thermograms of PE/PS samples with ωPS = 0.14 (1), 0.49 (2) and 0.8 (3). Heating rate 5 deg/min. Figure 11. Thermograms of PE/PS samples with ωPS = 0.14 (1), 0.49 (2) and 0.8 (3). Heating rate 5 deg/min.

With the increase of graft degree (Figure 11) up to ωPS = 0.49, and then up to 0.8 PS fraction,Table 5. Melting glass transition enthalpy (Δ isH observedm) values for in all the samples. temperature range of 29 ÷ 50 ◦C, the glass ◦ transition temperature is 42.7 C, and the heatHeating capacity Rate jump is −0.262 J/g·K. The melting ◦ temperatureSample of the5 deg/min crystalline phase of 10 the deg/min copolymer corresponds20 to deg/min 108 C, the melting enthalpy is 37.33 J/g. The values of melting enthalpy for all samples are presented 1st Heating 1st Heating 2nd Heating 1st Heating 2nd Heating in Table5. PE/PS16 71.0 78.41 69.24 78.26 69.59

TablePE/PS26 5. Melting enthalpy62.89 (∆ Hm) values58.76 for all samples.67.27 83.17 PE/PS47 56.11 42.62 47.15 51 57.75 PE/PS96 44.58 34.54 Heating40.44 Rate 36.7 48.38 PE/PS248Sample 5 deg/min25.38 21.19 10 deg/min23.03 26 20 deg/min 25.44 PE/PS271 1st Heating24.76 1st Heating25.44 2nd24.48 Heating 1st Heating28.45 2nd27.66 Heating PE/PS348PE/PS16 20.93 71.0 78.41 14.22 69.2416.43 78.2617.64 69.5922.58 PE/PS405PE/PS26 62.8919.19 58.76 21.35 67.2718.42 83.1721.38 21.34 PE/PS47 56.11 42.62 47.15 51 57.75 PE/PS96According to the 44.58 results of the 34.54 thermochemical 40.44 tests, we 36.7obtained unusual 48.38 infor- PE/PS248 25.38 21.19 23.03 26 25.44 mation about the effect of the composition of graft copolymer on its degree of crystallinity PE/PS271 24.76 25.44 24.48 28.45 27.66 andPE/PS348 glass transition 20.93temperature. As 14.22 an example, Figures 16.43 12 and 13 17.64 show the dependences 22.58 of PE/PS405these parameters 19.19on the composition 21.35 of the graft 18.42 polymer. First, 21.38 it can be seen 21.34 that, with an increase in the proportion of graft PS, both the melting temperature of the copolymer and the crystallinity degree of the PE phase decrease. In this case, the greatest effect is According to the results of the thermochemical tests, we obtained unusual information observed in the change in the crystallinity degree, less for the melting temperature. Thus, about the effect of the composition of graft copolymer on its degree of crystallinity and if the PE crystallinity degree in the initial state is ~54%, the crystallinity degree for the glass transition temperature. As an example, Figures 12 and 13 show the dependences of graft polymer with 70 wt.% PS content is ~10%, whereas the melting temperature of the these parameters on the composition of the graft polymer. First, it can be seen that, with graft polymer decreases by only six degrees. Second, it should be noted that the experi- an increase in the proportion of graft PS, both the melting temperature of the copolymer andmentally the crystallinity recorded glass degree transition of the PEtemperatur phase decrease.e of the graft In this polymer, case, the which greatest characterizes effect is observedthe segmental in the mobility change inin thethe crystallinityamorphous phase degree, of less the forgraft the polymer, melting temperature.practically does Thus, not

Polymers 2021, 13, 2512 15 of 18

if the PE crystallinity degree in the initial state is ~54%, the crystallinity degree for the graft PolymersPolymers 2021 2021, ,13 13, ,x x FOR FOR PEER PEER REVIEW REVIEWpolymer with 70 wt.% PS content is ~10%, whereas the melting temperature of the1717 graft of of 20 20

polymer decreases by only six degrees. Second, it should be noted that the experimentally recorded glass transition temperature of the graft polymer, which characterizes the segmen- changetalchange mobility with with inchanges changes the amorphous in in its its composition composition phase of thein in cont graftcontrastrast polymer, to to the the glass practicallyglass transition transition does temperature temperature not change withcal- cal- culatedchangesculated by by in the itsthe compositionFlory-Fox Flory-Fox equation equation in contrast (Figure (Figure to the 14). 14). glass We We transitionattribute attribute this temperaturethis effect effect to to calculatedthe the constancy constancy by theof of theFlory-Foxthe composition composition equation and and (Figure the the molecular molecular 14). We attributeweight weight of of this the the effectgraft graft topolymer polymer the constancy phase. phase. of the composition and the molecular weight of the graft polymer phase.

Figure 12. Generalized dependence of the crystallinity degree of the graft copolymer on the PS FigureFigure 12. 12. Generalized Generalized dependence dependence of of the the crystallinity crystallinity de degreegree of of the the graft graft copolymer copolymer on on the the PS PS frag- frag- mentfragmentment content. content. content.

FigureFigureFigure 13. 13. Dependence Dependence ofof of thethe the melting melting melting temperature temperature temperature of of graftof gr graft copolymersaft copolymers copolymers on theon on contentthe the content content of PS of fragments.of PS PS frag- frag- ments.ments.

Polymers 2021, 13, x FOR PEER REVIEW 18 of 20 Polymers 2021, 13, 2512 16 of 18

Figure 14. Generalized dependence of glass transition temperature on the composition of graft Figure 14. Generalized dependence of glass transition temperature on the composition of graft co- copolymer. The dashed line is plotted according to the Flory-Fox equation. polymer. The dashed line is plotted according to the Flory-Fox equation. We assume that the spontaneous destruction (melting) of PE crystallites and the We assume that the spontaneous destruction (melting) of PE crystallites and the en- enrichment of the amorphous phase of graft polymer with fragments of its macromolecules richment of the amorphous phase of graft polymer with fragments of its macromolecules occurs in the process of graft polymerization. The driving force of this process is the occursosmotic in pressurethe process exerted of graft by the polymerization. phase network The of crystallites driving force on theof this growing process phase is the of graftos- moticPS. The pressure value ofexerted this pressure by the phase can probably network be of estimated crystallites from on the growing value of pressurephase of (force)graft PS.required The value to expand of this pressure the sample can volumeprobably by be a estimated degree of from swelling the value and growthof pressure of the (force) graft requiredcopolymer, to expand which wethe assume sample to volume do in the by future.a degree of swelling and growth of the graft copolymer, which we assume to do in the future. 4. Conclusions 4. ConclusionsThus, based on the results obtained, we can assume that the formation of the graft PE-PSThus, copolymer based on involves the results three obtained, processes we occurring can assume simultaneously: that the formation of the graft PE-PS(1) Thecopolymer formation involves of radicals three andprocesses graft of occurring styrene to simultaneously: the amorphous PE phase; (1)(2) TheThe formation formation of ofradicals radicals and and graft graft of styrene of styrene to the to amorphous the PE chains, PE whichphase; are on the (2) Thesurface formation of the of crystallites; radicals and graft of styrene to the PE chains, which are on the sur- (3) faceThe of formation the crystallites; of a heterogeneous PS-PE system with a complex phase organization. (3) TheThe formation ﬁrst process of a proceeds heterogeneous with a constantPS-PE system composition with a complex of the copolymer, phase organization. which is in theThe amorphous first process phase. proceeds The second with leadsa constant to a decrease composition of the of crystallinity the copolymer, degree, which and is thein thetotal amorphous degree of phase. graft increases The second due leads to this to process.a decrease The of thirdthe crystallinity one is accompanied degree, and by the the totalgrowth degree of the of graftgraft copolymerincreases due phase to ofthis certain process. compositions. The third one is accompanied by the growth of the graft copolymer phase of certain compositions. Author Contributions: A.E.C.—Conceptualization, Methodology, Project administration, Data cura- Authortion, Formal Contributions: analysis, Writing A.E.C.—Conceptualization, and editing, V.A.T.—Conceptualization, Methodology, Project Methodology administration, and Writing Data cu- and ration,editing, Formal U.V.N.—Investigation, analysis, Writing and Data editing, curation, V.A.T.—Conceptualization, Writing and editing, A.D.A., Methodology V.K.G., V.Y.S., and Writing R.R.K.— andInvestigation. editing, U.V.N.—Investigation All authors have read, Data and agreedcuration, tothe Writing published and versionediting, of A.D.A., the manuscript. V.K.G., V.Y.S., R.R.K.—Investigation.Funding: This work was All authors supported have by read the Ministry and agreed of Science to the published and Higher version Education of the of manuscript. the Russian Funding:Federation This (project work was 0081-2019-0019). supported by the Ministry of Science and Higher Education of the Russian Federation (project 0081-2019-0019).

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Institutional Review Board Statement: The work was approved by the IPCE RAS expert council. Expert opinion number 191-21 of 16 July 2021. Informed Consent Statement: Informed consent was obtained from all subjects involved in the study. Data Availability Statement: The data presented in this study are available on request from the corresponding author. Acknowledgments: The authors would like to thank the Center for Collective Use of Scientific Equipment of the Frumkin Institute of Physical chemistry and Electrochemistry Russian academy of Sciences (IPCE RAS, Russia) for some measurements taken using the Center’s equipment. Conflicts of Interest: The authors declare no conflict of interest.

References 1. Krul, L.P.; Polikarpov, A.P. Progress in the synthesis of grafted materials using radiation graft polymerisation. Russ. Chem. Rev. 1990, 59, 469–481. [CrossRef] 2. Benson, R.S. Use of radiation in biomaterials science. Nucl. Instrum. Methods Phys. Res. B 2002, 191, 752–757. [CrossRef] 3. Kattan, M.; El-Nesr, E. Gamma-Radiation-induced graft copolymerization of acrylic acid onto poly(ethylene terephthalate) films: A study by thermal analysis. J. Appl. Polym. Sci. 2006, 102, 198–203. [CrossRef] 4. Kang, K.; Kang, P.H.; Nho, Y.C. Preparation and characterization of a proton-exchange membrane by the radiation grafting of styrene onto polytetrafluoroethylene films. J. Appl. Polym. Sci. 2006, 99, 1415–1428. [CrossRef] 5. Haslam, J.; Willis, H.A. Identification and Analysis of Plastics; Iliffe Books Ltd.: London, UK, 1965. 6. Shevlyakova, N.V.; D’yakova, M.G.; Luzina, N.N.; Semenov, V.I.; Shifrina, R.R.; Tverskoi, V.A.; Pravednikov, A.N. Post-radiation grafting of styrene to polyethylene film and distribution of grafted polystyrene. Polym. Sci. USSR 1987, 29, 348–353. [CrossRef] 7. Ranly, B.; Rabek, J.F. ESR Spectroscopy in Polymer Research; Springer: Berlin/Heidelberg, Germany, 1977. 8. Dechant, J.; Danz, R.; Kimmer, W.; Schmolke, R. Ultrarotspektroskopische Untersuchungen an Polymeren; Akademie-Verlag: Berlin, Germany, 1972. 9. Safronova, E.Y.; Golubenko, D.V.; Shevlyakova, N.V.; D’yakova, M.G.; Tverskoi, V.A.; Dammak, L.; Grande, D.; Yaroslavtsev, A. New cation-exchange membranes based on cross-linked sulfonated polystyrene and polyethylene for power generation systems. J. Membr. Sci. 2016, 515, 196–203. [CrossRef] 10. Sproll, V.; Nagy, G.; Gasser, U.; Embs, J.P.; Obiols-Rabasa, M.; Schmidt, T.J.; Gubler, L.; Balog, S. Radiation Grafted Ion-Conducting Membranes: The Influence of Variations in Base Film Nanostructure. Macromolecules 2016, 49, 4253–4264. [CrossRef] 11. Ferreira, L.M.; Falcão, A.N.; Gil, M.H. Modification of LDPE molecular structure by gamma irradiation for bioapplications. Nucl. Instrum. Methods Phys. Res. B 2005, 236, 513–520. [CrossRef] 12. Ranogajec, F.; Mlinac-Mišak, M. Improvement of the polymer stability by radiation grafting. Radiat. Phys. Chem. 2004, 71, 227–231. [CrossRef] 13. Tverskoi, V.A.; Semenov, V.I.; Shevlyakova, N.V.; Buzin, A.V.; Zamyslov, R.A.; Dobrov, I.V.; Pravednikov, A.N. Structure of structurally inhomogeneous sulphocationic membranes and their gas permeability. Polym. Sci. USSR 1988, 30, 2778–2783. [CrossRef] 14. Zhilyaeva, N.A.; Lytkina, A.A.; Mironova, E.Y.; Ermilova, M.M.; Orekhova, N.V.; Shevlyakova, N.V.; Tverskoy, V.A.; Yaroslavtsev, A.B. Polyethylene with radiation-grafted sulfonated polystyrene membranes for butane and butenes separation. Chem. Eng. Res. Des. 2020, 161, 253–259. [CrossRef] 15. Zhilyaeva, N.; Mironova, E.; Ermilova, M.; Orekhova, N.; Dyakova, M.; Shevlyakova, N.; Tverskoii, V.; Yaroslavtsev, A. Facilitated transport of ethylene through the polyethylene-graft-sulfonated polystyrene membranes. The role of humidity. Sep. Purif. Technol. 2018, 195, 170–173. [CrossRef] 16. Zhilyaeva, N.A.; Mironova, E.Y.; Ermilova, M.M.; Orekhova, N.V.; Bondarenko, G.N.; Dyakova, M.G.; Shevlyakova, N.V.; Tverskoy, V.A.; Yaroslavtsev, A.B. Polyethylene-graft-sulfonated polystyrene membranes for the separation of ethylene-ethane mixtures. Pet. Chem. 2016, 56, 1034–1041. [CrossRef] 17. Aleksandrova, L.B.; Shifrina, R.R.; Gil’man, A.B.; Shevlyakova, N.V.; D’yakova, M.G.; Tverskoi, V.A. Analysis of the distribution of graft polymer in a polymer substrate by IR spectroscopy. Polym. Sci. USSR 1983, 25, 1539–1541. [CrossRef] 18. Elazmirly, M.A.; Zahran, A.H.; Barakat, M.F. Radiation-induced graft copolymerization of styrene on to nylon-6 via various routes. Eur. Polym. J. 1975, 11, 19–24. [CrossRef] 19. O’Neill, T. Grafting of acrylic acid onto radiation-peroxidized polypropylene film in the presence of ferrous ion. J. Polym. Sci. A Polym. Chem. 1972, 10, 569–580. [CrossRef] 20. Bershtein, V.A.; Egorov, V.M. Differential Scanning Calorimetry in Physics and Chemistry of Polymers; Khimiya: St. Petersburg, FL, USA, 1990. (In Russian) 21. Gedde, U.W.; Hedengvist, M.S. Fundamental Polymer Science, 2nd ed.; Springer Nature Switzerland & AG: Cham, Switzerland, 2019. 22. Shcherbina, A.A.; Chalykh, A.E. Adhesion and Autohesion of Polymers. In Transitional Zones. Phase Equilibria. Inter- and Self-Diffusion; Sam Polygraphist: Moscow, Russia, 2018; ISBN 978-5-00077-803-6. (In Russian) Polymers 2021, 13, 2512 18 of 18

23. Kinloch, A.J. Adhesion and Adhesives: Science and Technology; Chapman and Hall: London, UK, 1987; p. 441. ISBN 0-412-27440-X. 24. Golding, B. Polymers and Resins: Their Chemistry and Chemical Engineering; D. Van Nostrand Company: New York, NY, USA, 1959. 25. Arakawa, K.; Seguchi, T.; Watanabe, Y.; Haykawa, N.; Kuniyama, I.; Machi, S. Dose-rate effect on radiation-induced oxidation of polyethylene and ethylene-propylene co-polymer. J. Polym. Sci. A Polym. Chem. 1981, 19, 2123–2125. [CrossRef] 26. Kiryushkin, S.G.; Dalinkevich, A.A.; Shlyapnikov, Y.A. Concentration distribution of oxygen containing groups in radiation oxidized polyethylene. Polym. Sci. USSR 1988, 30, 1527–1533. [CrossRef] 27. Chalykh, A.E.; Nikulova, U.V.; Shcherbina, A.A.; Matveev, V.V. Phase equilibria in a polyethylene-polystyrene system. Polym. Sci. Ser. A 2017, 59, 107–115. [CrossRef] 28. Lisichkin, G.V. Chemistry of Grafted Surface Compounds; Fizmatlit: Moscow, Russia, 2003; ISBN 5-9221-0342-3. (In Russian) 29. Roldugin, V.I. Physicochemistry of the Surface: Textbook-Monograph, 2nd ed.; Intellect Publishing House: Dolgoprudny, Russia, 2011; ISBN 978-5-91559-116-4. (In Russian)